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Determining mean Length of Day and DeltaT formula

Using observed data for 500 BCE to 1600 CE from [Stephenson, 2004] and for 1650 CE to 1990 CE from IERS, in the below section the change in LOD and Delta T are described.

Mean Length of Day (LOD)

The following mean changes in Length of Day (LOD) are depicted in the below figure:

Observed mean changes in LOD (pink wavy line) (from 1650 CE is are quite accurate values)
Tidal friction influence (straight light blue dotted line) of 2.3 [ms/cy] [Stephenson, 1997, page 513]
Optimized mean changes in LOD (black crosses), this is as per my optimized function (using Simplex method with one linear and one periodic term).
The mean Solar Day function is also incorporated in the Excel XLA file for archaeoastronomy and geodesy functions.
Average mean changes in LOD (yellow straight line), is around 1.72 [ms/cy], using my own Simplex optimized function. This is within the value range (1.70+/-0.05 [ms/cy]) as provided in Stephenson ([1997], page 514)

Interesting to see that there looks to be a periodicy of around 1440 and 1550 years (also mentioned by Stephenson ([1997], page 516), if people know such a cycle and have some proof due to an astronomical/geophysical process, let me know.
It could be this periodicy is caused by the splining methodology used (based on the ideas of Slutzky [1937]), but I doubt that.
Another reason for a spurious periodicy could be due to the sampling of only a limited amount of eclipses (Stephenson's pool of observations), but I think that that would not results in such a long term periodicy, because:

I am thinking that the Nyquist-Shannon theory of sampling and low pass (anti-aliasing) filtering could be related to this idea. If this low pass filtering does not happen at half the Nyquist sampling frequency one could get spurious frequencies (f_sample +/- f_actual) in the relating analysis.
Assuming say an on average sampling of every 6 years an eclipse (pool of 400 observations over a period of 2300 years).
to get a spurious periodicy of 1550 years in an analysis, an actual periodicy of some 5.98 or 6.02 years (1/1550 = 1/6 +/- 1/actual) must exist in the real LOD (which is not 'filtered out'). Such a natural(/actual) periodicy is not likely, IMHO.
furthermore the splining in 5 knots would also not stimulate such a long term periodicy over all knot intervals (the spurious periodicy would even vary much more per knot interval; because the amount of observations varies greatly per knot interval).
In the above I used a uniform distribution of the observation, while in actual live it are random observations, but still the large variation of observation per knot interval would not give such a visible uniform long term periodicy over all knot intervals.
A test, if this periodicy is spurious, is by deliberately changing the number of observations (larger spacing between observations) and see if the periodicy changes in duration. If it is spurious, the periodicy must change according to the (1/spurious = 1/sample +/- 1/actual) formula.

Linking the seen periodicy with possible geophysical events

Stephenson [Stephenson, 1997, page 513] gives an possible explanation what causes the periodicy:

With regard to the quasi-periodic fluctuations on a timescale of some 1500 years, a possible mechanism would appear to be electromagnetic coupling between the core and the mantle of the Earth. This is the most likely cause of the decade fluctuations (Lambeck, 1980, p. 247).

Another possible reason he gives is the change of sea-level variations (Lamb, 1982); "as significant long-term alterations in climate have been detected in the last few milennia".

Another reason might be the Dansgaard-Oeschger (DO) warming events, (with a possible solar origin) which are events spaced by 1470 years (which is close to my determined periodicy value of 1440 and 1550 years).
The astronomical year of a DO warming event is on -9658 - 1473*event#
With: event# = an positive/negative integer

The periodicy of DeltaT seems to reach zero around 1820 CE, so that would be a DO warming event# around -7 or -8 (-7.8 to be specific).

Mean Delta T

The below mean DeltaT graph is determined using the my above change in LOD formula. The following graphs are depicted:

Observed mean DeltaT (pink line)
DeltaT due to tidal friction influence (straight light blue dotted line) [Stephenson, 1997, page 513]
Optimized mean DeltaT (black crosses), this is as per the integral of my change in LOD function
This mean DeltaT function is also incorporated in the Excel XLA file for archaeoastronomy and geodesy functions.
The average mean DeltaT (yellow line) based on LOD change of around 1.7 [ms/cy] is also depicted

Conclusion

The parabolic formula provided by Stephenson to calculate the mean DeltaT is perhaps lacking enough elements to predict the DeltatT (or LOD) accurate enough over the whole time period of 500 BCE to say 1300 CE (differences smaller than 10%). This additional periodic term in the formula gives a better accuracy then only a parabolic formula.
If you want to test the formula (one can use Excel XLA file), let me know.

The DeltaT formula

'using Stephenson&Morrison [2004] as the basis (n.dot = -26"/cy^2):
StartYear = 1820 [year]
Average = 1.80 [msec/cy]
Periodicy = 1443 [year]
Amplitude = 3.76 [msec]
Y2D = 365.25
OffSetYear = (JDutfromDate(StartYear, 0) - JDNDays) / 365.25
DeltaT_VR = (OffSetYear ^ 2 / 100 / 2 * Average + Periodicy / 2 / Pi * Amplitude * (Cos((2 * Pi * OffSetYear / Periodicy)) - 1)) * Y2D [msec]

More generally used formula (although Stephenson's table look is better [or above formula which follows the table better]):
COD is the LOD Change (normally: 1.7 [msec/cy])
DeltaT = OffSetYear ^ 2 / 100 / 2 * COD * Y2D [msec]

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